I went to Hajj with my young daughter and I intended Tamattu' Hajj for her, but I did not slaughter because someone told me that it is permissible not to slaughter. What is the ruling on that?
All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His Slave and Messenger.
The one who performs Tamattu' Hajj is liable to slaughter a sacrifice if he is able. If he cannot, he should fast three days in Hajj and seven when he returns to his family. This applies to adults as well as children. As for children, their guardian should fast on their behalf. If anyone says other than that, he is mistaken.
Allah Knows best.